@article{EJP904,
author = {Juerg Huesler and Vladimir Piterbarg and Yueming Zhang},
title = {Extremes of Gaussian Processes with Random Variance},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Gaussian processes; locally stationary; ruin probability; random variance; extremes; fractional Brownian motions},
abstract = {Let $\xi(t)$ be a standard locally stationary Gaussian process with covariance function $1-r(t,t+s)\sim C(t)|s|^\alpha$ as $s\to0$, with $0<\alpha\leq 2$ and $C(t)$ a positive bounded continuous function. We are interested in the exceedance probabilities of $\xi(t)$ with a random standard deviation $\eta(t)=\eta-\zeta t^\beta$, where $\eta$ and $\zeta$ are non-negative bounded random variables. We investigate the asymptotic behavior of the extreme values of the process $\xi(t)\eta(t)$ under some specific conditions which depends on the relation between $\alpha$ and $\beta$.},
pages = {no. 45, 1254-1280},
issn = {1083-6489},
doi = {10.1214/EJP.v16-904},
url = {http://ejp.ejpecp.org/article/view/904}}